Linear differential operators on contact manifolds
Mathematical Physics
2019-01-01 v1 Differential Geometry
math.MP
Abstract
We consider differential operators between sections of arbitrary powers of the determinant line bundle over a contact manifold. We extend the standard notions of the Heisenberg calculus: noncommutative symbolic calculus, the principal symbol, and the contact order to such differential operators. Our first main result is an intrinsically defined "subsymbol" of a differential operator, which is a differential invariant of degree one lower than that of the principal symbol. In particular, this subsymbol associates a contact vector field to an arbitrary second order linear differential operator. Our second main result is the construction of a filtration that strengthens the well-known contact order filtration of the Heisenberg calculus.
Cite
@article{arxiv.1205.6562,
title = {Linear differential operators on contact manifolds},
author = {Charles H. Conley and Valentin Ovsienko},
journal= {arXiv preprint arXiv:1205.6562},
year = {2019}
}